A global Torelli theorem for singular symplectic varieties
A global Torelli theorem for singular symplectic varieties
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DOI：
10.4171/jems/1026
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发表时间：
2016-12
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通讯作者：
Benjamin Bakker;C. Lehn
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文献类型：
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作者：
Benjamin Bakker;C. Lehn
本文系统地研究了具有不可约辛流形分解的奇异辛簇的模理论，并证明了Verbitsky整体Torelli定理的一个类似定理。代替扭量线，Verbitsky关于遍历复结构的工作提供了必要的全局输入。一方面，我们的形变理论结果是Huybrechts关于双有理超Kahler流形形变等价定理在奇异辛簇上的进一步推广.另一方面，我们的整体模理论提供了一个框架，用于理解和分类辛奇点，产生于不可约辛流形的双有理压缩，并有一些应用到$K3^{[n]}$-型品种。
We systematically study the moduli theory of singular symplectic varieties which have a resolution by an irreducible symplectic manifold and prove an analog of Verbitsky's global Torelli theorem. In place of twistor lines, Verbitsky's work on ergodic complex structures provides the essential global input. On the one hand, our deformation theoretic results are a further generalization of Huybrechts' theorem on deformation equivalence of birational hyperkahler manifolds to the context of singular symplectic varieties. On the other hand, our global moduli theory provides a framework for understanding and classifying the symplectic singularities that arise from birational contractions of irreducible symplectic manifolds, and there are a number of applications to $K3^{[n]}$-type varieties.